Single Cell Grey Scatterometry Overlay Targets and Their Measurement Using Varying Illumination Parameter(s)

ABSTRACT

Scatterometry overlay (SCOL) measurement methods, systems and targets are provided to enable efficient SCOL metrology with in-die targets. Methods comprise generating a signal matrix by: illuminating a SCOL target at multiple values of at least one illumination parameter, and at multiple spot locations on the target, wherein the illumination is at a NA (numerical aperture) &gt;⅓ yielding a spot diameter &lt;1μ, measuring interference signals of zeroth and first diffraction orders, and constructing the signal matrix from the measured signals with respect to the illumination parameters and the spot locations on the target; and deriving a target overlay by analyzing the signal matrix. The SCOL targets may be reduced to be a tenth in size with respect to prior art targets, as less and smaller target cells are required, and be easily set in-die to improve the accuracy and fidelity of the metrology measurements.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. application Ser. No. 16/491,963filed Sep. 6, 2019, which is a national stage of PCT/US2019/045039 filedAug. 5, 2019, which claims priority to the provisional patentapplication filed Nov. 21, 2008 and assigned U.S. App. No. 62/770,680,the disclosures of which are hereby incorporated by reference.

BACKGROUND OF THE INVENTION 1. Technical Field

The present invention relates to the field of semiconductor metrology,and more particularly, to scatterometry overlay (SCOL) targets andmetrology modules and methods for measuring them.

2. Discussion of Related Art

Typical SCOL metrology utilizes multiple cells having multiple periodicstructures in corresponding layers, which are displaced with respect toeach other by predetermined offsets to enable the derivation of theoverlay from differential signals between the cells.

SUMMARY OF THE INVENTION

The following is a simplified summary providing an initial understandingof the invention. The summary does not necessarily identify key elementsnor limit the scope of the invention, but merely serves as anintroduction to the following description.

One aspect of the present invention provides scatterometry overlay(SCOL) measurement method comprising: generating a signal matrix by:illuminating a SCOL target at multiple values of at least oneillumination parameter, and at multiple spot locations on the target,wherein the illumination is at a NA (numerical aperture) >⅓ yielding aspot diameter <1μ, measuring interference signals of zeroth and firstdiffraction orders, and constructing the signal matrix from the measuredsignals with respect to the illumination parameters and the spotlocations on the target; and deriving a target overlay by analyzing thesignal matrix.

These, additional, and/or other aspects and/or advantages of the presentinvention are set forth in the detailed description which follows;possibly inferable from the detailed description; and/or learnable bypractice of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of embodiments of the invention and to showhow the same may be carried into effect, reference will now be made,purely by way of example, to the accompanying drawings in which likenumerals designate corresponding elements or sections throughout.

In the accompanying drawings:

FIGS. 1A and 1B are high-level schematic illustrations of SCOL targetsand respective measurement systems, according to some embodiments of theinvention

FIG. 2 is a schematic illustration of a SCOL target and its measurementprocedure, according to the prior art.

FIG. 3 is a high-level flowchart illustrating a method, according tosome embodiments of the invention.

DETAILED DESCRIPTION OF THE INVENTION

In the following description, various aspects of the present inventionare described. For purposes of explanation, specific configurations anddetails are set forth in order to provide a thorough understanding ofthe present invention. However, it will also be apparent to one skilledin the art that the present invention may be practiced without thespecific details presented herein. Furthermore, well known features mayhave been omitted or simplified in order not to obscure the presentinvention. With specific reference to the drawings, it is stressed thatthe particulars shown are by way of example and for purposes ofillustrative discussion of the present invention only, and are presentedin the cause of providing what is believed to be the most useful andreadily understood description of the principles and conceptual aspectsof the invention. In this regard, no attempt is made to show structuraldetails of the invention in more detail than is necessary for afundamental understanding of the invention, the description taken withthe drawings making apparent to those skilled in the art how the severalforms of the invention may be embodied in practice.

Before at least one embodiment of the invention is explained in detail,it is to be understood that the invention is not limited in itsapplication to the details of construction and the arrangement of thecomponents set forth in the following description or illustrated in thedrawings. The invention is applicable to other embodiments that may bepracticed or carried out in various ways as well as to combinations ofthe disclosed embodiments. Also, it is to be understood that thephraseology and terminology employed herein are for the purpose ofdescription and should not be regarded as limiting.

Unless specifically stated otherwise, as apparent from the followingdiscussions, it is appreciated that throughout the specificationdiscussions utilizing terms such as “processing”, “computing”,“calculating”, “determining”, “enhancing”, “deriving” or the like, referto the action and/or processes of a computer or computing system, orsimilar electronic computing device, that manipulates and/or transformsdata represented as physical, such as electronic, quantities within thecomputing system's registers and/or memories into other data similarlyrepresented as physical quantities within the computing system'smemories, registers or other such information storage, transmission ordisplay devices. In certain embodiments, illumination technology maycomprise, electromagnetic radiation in the visual range, ultraviolet oreven shorter wave radiation such as x rays, and possibly even particlebeams.

Embodiments of the present invention provide efficient and economicalmethods and mechanism for scatterometry overlay (SCOL) metrologymeasurements and thereby provide improvements to the technological fieldof semiconductor metrology. Scatterometry overlay (SCOL) measurementmethods, systems and targets are provided to enable efficient SCOLmetrology with in-die targets. Methods comprise generating a signalmatrix by: illuminating a SCOL target at multiple values of at least oneillumination parameter, and at multiple spot locations on the target,wherein the illumination is at a NA (numerical aperture) >⅓ yielding aspot diameter <1μ, measuring interference signals of zeroth and firstdiffraction orders, and constructing the signal matrix from the measuredsignals with respect to the illumination parameters and the spotlocations on the target; and deriving a target overlay by analyzing thesignal matrix. The SCOL targets may be reduced to be a tenth in sizewith respect to prior art targets, as less and smaller target cells arerequired, and be easily set in-die to improve the accuracy and fidelityof the metrology measurements. The small spots, the use of varyingillumination parameters and quick spot scanning methods, enable usingsingle cells instead on pairs of cells with opposite predefined offsets,and enable reducing the cell size together with the spot size reduction.

FIGS. 1A and 1B are high-level schematic illustrations of a SCOL target110 and its measurement system 100, according to some embodiments of theinvention. System 100, e.g., a metrology system or module therewithin,may be configured to illuminate SCOL target 110 having periodicstructures 120A, 120B (e.g., gratings) using a large NA (numericalaperture) illumination unit 130 (e.g., having NA>⅓ such as any ofNA=0.4, 0.5. 0.6, 0.7, 0.8, 0.9, or other values—with orders −1, 0 and+1 at least partly overlapping 145A in the pupil plane) resulting incorresponding small illumination spots 136, e.g., smaller than 1μ, orpossibly between any of 250-1000 nm or 600-1000 nm. In FIG. 1A, SCOLtarget 110 is illustrated in schematic cross-section view, withintermediate layers between top periodic structure 120A and bottomperiodic structure 120B, and notation of illumination 135, reflectionsignal (R₀ denoting the zeroth order) and ±1 order diffracted signals145, denoted by T_(±1) and B_(±1) for top and bottom ±1 diffractionorders, respectively. In FIG. 1B, SCOL target 110 is illustrated inschematic top view, and may have an offset (not shown) between periodicstructures 120A, 120B.

System 100 may be configured to illuminate SCOL target 110 at aplurality of spot locations 136 on target 110, which may be steppedalong the measurement direction(s) of periodic structure(s) 120A, 120Bof SCOL target 110 and possibly scanned along the elements of periodicstructure(s) 120A, 120B (perpendicular to the measurement direction) foraveraging the measured signals. Spot locations 136 may be selected to bewithin a pitch of periodic structure(s) 120A, 120B of SCOL target 110,as illustrated schematically in FIG. 1B. It is noted that spot locations136 may be spread over two or more pitches, yet at least two of the spotlocations should be not equivalent with respect to the targetperiodicity, to yield non-equivalent signals for analysis. Selectingspot locations 136 within one (or two) target pitches enables asignificant reduction in target size, compared with prior art thatrequires many target pitches to be covered by the large prior artillumination spot.

System 100 further comprises a measurement unit 140 with pupil planesensor(s) configured to measure a corresponding plurality of measurementsignals 145 from multiple spot locations 136 on target 110. Signals 145comprise interference signals of zeroth and first order diffractionscomponents of the illumination from each spot location 136, asillustrated schematically by overlaps 145A in FIGS. 1A and 1B. Suchinterference is due to using small illumination spots 135 andmeasurement may utilize changes in signal intensity to isolate orevaluate first order signal fluctuations from background zeroth orderreflections. SCOL targets 110 may comprise a single cell, from which allsignals may be derived and the corresponding overlay may be calculated.Analysis of signals 145 may be carried out as taught by U.S. PatentApplication Publication No. 2017/0268869, which is incorporated hereinby reference in its entirety.

System 100 may be configured to carry out illumination 130 at least attwo different illumination parameters (denoted as “grey” SCOL), e.g.,using multiple different wavelengths (e.g., three or more), usingdifferent focus and/or positions (possibly involving scanning thetarget), different polarizations, etc., and to derive the target overlayfrom an analysis of measured signals 145 with respect to the spotlocations on target 110 and the illumination parameters. It is notedthat one, two, three or more illumination parameters may be used in themeasurements, in certain embodiments, using three illumination parametervalues was found to be optimal in some cases with respect to measurementand overlay derivation complexities.

System 100 further comprises a processing unit 155 configured toconstruct a signal matrix 150 from measured signals 145 with respect tothe illumination parameters and the spot locations on target 110, and toderive the target overlay by analyzing signal matrix 150. Asmeasurements employ multiple small spots 135, having differentillumination characteristics, to multiple spot locations 136 on target110 that yield interfered (mixed) diffraction orders from correspondingsignals 145—resulting signal matrix 150 may be used to derive andanalyze the signals 147 with respect to spot locations 136 andilluminating characteristics to derive the target overlay.

System 100 may be further configured to calibrate signal matrix 150 byperforming or simulating measurements of SCOL targets with known overlayvalues. For example, multiple reference targets, possibly on referencewafer(s), with known overlays may be measured by system 100 and themeasurements may be used to generate a model relating measurementresults to the known overlays. Alternatively or complementarily,simulations may be used to suggest relations between overlays andsignals, and possibly to optimize the illumination parameters used(e.g., wavelengths values, other illumination parameters) as well asspot size and NA, stepping and scanning methods and parameters of spots135 over target 110 etc. System 100 may be further configured to createa model of signal matrix 150 with respect to spot locations 136,illumination parameters and target overlays. Calibration may be carriedout in a training phase or on-the-fly. Scanning targets 110 with smallspots 135 may be carried out, e.g., by scanning over a length scale ofone target pitch (or, e.g., two target pitches), e.g., smaller than 1μ.

In certain embodiments, target 110 may be designed to have periodicstructures with specified pitches along two measurement directions, andsystem 100 may be configured to derive measurements using the same cellfor both directions, with corresponding signal matrices 150 derived foreach direction, possibly simultaneously, and analyzed to deriverespective overlays as disclosed above.

In various embodiments, a formalism may be used to derive the relationbetween the overlay and the measurement results with multipleillumination parameters, based e.g., on electromagnetic modelling and/orsimulation of optical path differences (OPDs), that relate changes inthe strength of the diffracted fields with the changing illuminationparameters—with respect to the overlay. Following correspondinganalysis, simulation and/or training, direct relations may beestablished between the overlay and the measurement results.

For example, the inventors have noted that the ratio of the sum ofdifferential signals to the difference of signal sums in the twomeasurement wavelengths depends only on the difference between the OPDsat the two wavelengths (or generally at the two measurement conditions),and not on the OPDs themselves. Therefore, in certain embodiments, thisexpression may be a stable parameter between process variations. Forexample, the measurement signals may be modelled while maintaining arelation between the illumination parameters and intensity measurementsand/or accuracy metrics associated therewith.

In certain embodiments, landscape shifts with process variation may beutilized to derive overlays and/or to decouple between the overlay andtarget asymmetries, landscapes comprising an at least partiallycontinuous dependency of at least one metrology metric on at least oneparameter, as taught e.g., by U.S. Application Publication Nos.2016/0313658 and 2018/0023950, incorporated herein by reference in theirentirety. For example, measurements may be carried out at flat andresonant regions of the landscape to derive the overlay (and/or processvariation). In certain embodiments, opposite predetermined offsets maybe set in single target at different sites on the wafer, and thederivation may take into account the relative effects of these intendedoffsets.

In certain embodiments, a training phase may include measuring themetrology measurement recipe over multiple sites across the wafer, andmodelling from the measurements, at least partly, the relation betweenthe changes in illumination parameters and the changes in OPDs—which maythen be used to derive the overlays. For example, certain wavelengthranges may be used for the measurements, with respect to certain rangesof changes in OPD.

FIG. 2 is a schematic illustration of a SCOL target 80 and itsmeasurement procedure 90, according to the prior art. Prior art SCOLtargets 80 typically comprise at least two cells 80A, 80B in eachmeasurement direction, which comprise two or more periodic structures incorresponding layers, which are displaced with respect to each other byopposite predetermined offsets +f₀ and −f₀, illustrated schematically.Cells 80A, 80B are used to extract the (unintended) overlay between theperiodic structures from measured diffraction signals from cells 80A,80B. Measurements 90 are carried out by providing illumination andmeasurement conditions which prevent overlap of the diffraction orders65 (e.g., +1^(st), −1^(st)) with the reflected illumination (zerothorder) at the pupil plane of a respective sensor 60. The required priorart illumination conditions (of illumination unit 70) include a smallnumerical aperture (NA) which creates a large illumination spot 75 oncells 80A, 80B, and provides the required diffraction order isolation onsensor 60. For example, small illumination NA (e.g., NA=0.1, 0.2, 0.3 orother values smaller than about a third—with orders −1, 0 and +1 notoverlapping in the pupil plane) may be configured to result inillumination spot 75 being 1μ or more, to ensure scattered ordersseparation. The overlay is then calculated from the differential signalbetween the cells 62. It is noted that large illumination spot 75requires prior art cells 80A, 80B to be large, and the minimalrequirement of two cells per direction (for providing the oppositepredetermined offsets ±f₀) further increases the size of prior art SCOLtargets 80, reaching typically e.g., 8μ×8μ (cell size) or larger.

Advantageously, the inventors have found out that in contrast to priorart, a single cell approach to SCOL is attainable using a smallillumination spot and multiple illumination parameter(s) values, such asmultiple wavelengths instead of using prior art cell pairs with oppositepredetermined offsets. For example, modification of illuminationparameters was found to be related to fluctuation in measured signalintensities (and/or related accuracy metrics), which were then used toderive data concerning the respective measured targets. Advantageously,the disclosed approach reduces significantly the real estate requiredfor the metrology target, possibly enabling in-die metrology—due tousing a single cell instead of two cells for each measurement directionand as the cells can be made smaller due to the use of a smallillumination spot. It is noted that that significant reduction in realestate is achieved at the cost of requiring measurements with multiplemeasurement parameters and possibly target scanning (which may takelonger and require illumination modification) and possibly at the costof making the calibration more empirical in nature, as the derivation ofthe overlay from the measurement data is less straightforward than inthe prior art. The derivation of the overlay from the calibratedmeasurements may be carried out analytically, e.g., using simulations,in a training phase, using calibration wafer(s) and/or using simulation.It is emphasized though, that following initial calibration andtraining, the derivation of the overlay is expected to be at least asfast as in the prior art.

According to initial modelling, in certain embodiments, SCOL targets 110may be significantly smaller than prior art SCOL targets 80—due to theirreduction to one cell 115 for each measurement direction (or possiblyusing the same cell for both directions) and optional reduction of cellsize due to using smaller spot 135. For example, single cell targets 110may be four or less pitch bars (periodic structure elements) wide,possibly one or two pitch bars wide. As a result, SCOL targets 110 maybe down to ten times smaller than prior art SCOL targets 80 (e.g.,measure 2μ×2μ or smaller, vs. 8μ×8μ or larger, respectively). Periodicstructures 120A, 120B in multiple layers of SCOL target 110 may bealigned, as prior art predefined offsets may not be necessary in thecurrent invention (they are used in the prior art to providedifferential signal 62, which may be presently replaced by signal matrix150). It is noted that multiple illumination characteristics may be usedin various embodiments to extract the overlay from the differentresponses of periodic structures 120A, 120B, rather than thepredetermined offsets used in the prior art.

Advantageously, disclosed small SCOL targets 110 are readily designed asin-die targets or marks, providing higher metrology accuracy andfidelity with respect to the semiconductor devices on the wafer.

In various embodiments, disclosed systems 100, targets 110 and methods200 may increase the illumination NA to provide signals including zerothand first order mixing, which is utilized by spot scanning to detect theresulting modulation (as the spot is scanned and/or as the illuminationcharacteristics are changed) in the overlapping orders over the pupilarea. Measurements with multiple wavelengths include information forderiving the overlay without the need for an additional cell. System 100may implement fast spot scanning and fast wavelength switching so thatthe data required for the disclosed measurements is collected withminimal or no MAM (move-acquire-measure) penalty relative to specifiedrequirements, and thereby enable in-die small targets required bycustomers.

FIG. 3 is a high-level flowchart illustrating a method 200, according tosome embodiments of the invention. The method stages may be carried outwith respect to SCOL targets 110 and/or measurement systems 100described above, which may optionally be configured to implement method200. Method 200 may be at least partially implemented by at least onecomputer processor, e.g., in a metrology module. Certain embodimentscomprise computer program products comprising a computer readablestorage medium having computer readable program embodied therewith andconfigured to carry out the relevant stages of method 200. Certainembodiments comprise metrology measurements derived by embodiments ofmethod 200. Method 200 may comprise the following stages, irrespectiveof their order.

Scatterometry overlay (SCOL) measurement method 200 comprises generatinga signal matrix (stage 240) by: illuminating a SCOL target, wherein theillumination is at a large NA (numerical aperture) >⅓ yielding a smallspot diameter <1μ (stage 210), at multiple spot locations on the target(stage 220), and at multiple values of at least one illuminationparameter (stage 230), e.g., three or more wavelengths, and measuringinterference signals of zeroth and first diffraction orders (stage 215).The signal matrix is then constructed from the measured signals withrespect to the illumination parameters and the spot locations on thetarget (stage 240). Method 200 further comprises deriving a targetoverlay by analyzing the signal matrix, e.g., from an analysis of themeasured signals with respect to the spot locations on the target andthe illumination parameters (stage 250).

The SCOL target may comprise at least one periodic structure and themultiple spot locations may be within one pitch (or two pitches) of theat least one periodic structure, so that non-equivalent spot locationswith respect to the periodicity of the target are used. The spotlocations on the target may be set within the target pitch along ameasurement direction of the at least one periodic structure, changingthe spot locations within the target pitch (stage 222), and the measuredsignal may be averaged in a direction perpendicular to the measurementdirection, e.g., by scanning the spots along the target elements (stage224).

In certain embodiments, SCOL measurement method 200 may further comprisecalibrating the signal matrix by performing or simulating measurementsof SCOL targets with known overlay values (stage 260).

In certain embodiments, SCOL measurement method 200 may further comprisecarrying out a training phase of measuring a corresponding metrologymeasurement recipe over multiple sites across the wafer (stage 270).

In certain embodiments, SCOL measurement method 200 may further comprisecreating a model of the signal matrix with respect to the spotlocations, illumination parameters and target overlays (stage 280).

In certain embodiments, method 200 as a SCOL target design method maycomprise designing the SCOL target as a single cell target and/or asbeing 2μ×2μ or smaller, and possibly placed in-die on a correspondingwafer. In certain embodiments, method 200 may further compriseconfiguring the periodic structures of the target to be aligned and/orbe at most four, three, or two pitch bars (periodic structure elements)wide, possibly even one pitch wide. Certain embodiments comprise targetdesign files of SCOL targets 110 and/or SCOL targets designed by theSCOL target design method.

Aspects of the present invention are described above with reference toflowchart illustrations and/or portion diagrams of methods, apparatus(systems) and computer program products according to embodiments of theinvention. It will be understood that each portion of the flowchartillustrations and/or portion diagrams, and combinations of portions inthe flowchart illustrations and/or portion diagrams, can be implementedby computer program instructions. These computer program instructionsmay be provided to a processor of a general-purpose computer, specialpurpose computer, or other programmable data processing apparatus toproduce a machine, such that the instructions, which execute via theprocessor of the computer or other programmable data processingapparatus, create means for implementing the functions/acts specified inthe flowchart and/or portion diagram or portions thereof.

These computer program instructions may also be stored in a computerreadable medium that can direct a computer, other programmable dataprocessing apparatus, or other devices to function in a particularmanner, such that the instructions stored in the computer readablemedium produce an article of manufacture including instructions whichimplement the function/act specified in the flowchart and/or portiondiagram or portions thereof.

The computer program instructions may also be loaded onto a computer,other programmable data processing apparatus, or other devices to causea series of operational steps to be performed on the computer, otherprogrammable apparatus or other devices to produce a computerimplemented process such that the instructions which execute on thecomputer or other programmable apparatus provide processes forimplementing the functions/acts specified in the flowchart and/orportion diagram or portions thereof.

The aforementioned flowchart and diagrams illustrate the architecture,functionality, and operation of possible implementations of systems,methods and computer program products according to various embodimentsof the present invention. In this regard, each portion in the flowchartor portion diagrams may represent a module, segment, or portion of code,which comprises one or more executable instructions for implementing thespecified logical function(s). It should also be noted that, in somealternative implementations, the functions noted in the portion mayoccur out of the order noted in the figures. For example, two portionsshown in succession may, in fact, be executed substantiallyconcurrently, or the portions may sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each portion of the portion diagrams and/or flowchart illustration,and combinations of portions in the portion diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

In the above description, an embodiment is an example or implementationof the invention. The various appearances of “one embodiment”, “anembodiment”, “certain embodiments” or “some embodiments” do notnecessarily all refer to the same embodiments. Although various featuresof the invention may be described in the context of a single embodiment,the features may also be provided separately or in any suitablecombination. Conversely, although the invention may be described hereinin the context of separate embodiments for clarity, the invention mayalso be implemented in a single embodiment. Certain embodiments of theinvention may include features from different embodiments disclosedabove, and certain embodiments may incorporate elements from otherembodiments disclosed above. The disclosure of elements of the inventionin the context of a specific embodiment is not to be taken as limitingtheir use in the specific embodiment alone. Furthermore, it is to beunderstood that the invention can be carried out or practiced in variousways and that the invention can be implemented in certain embodimentsother than the ones outlined in the description above.

The invention is not limited to those diagrams or to the correspondingdescriptions. For example, flow need not move through each illustratedbox or state, or in exactly the same order as illustrated and described.Meanings of technical and scientific terms used herein are to becommonly understood as by one of ordinary skill in the art to which theinvention belongs, unless otherwise defined. While the invention hasbeen described with respect to a limited number of embodiments, theseshould not be construed as limitations on the scope of the invention,but rather as exemplifications of some of the preferred embodiments.Other possible variations, modifications, and applications are alsowithin the scope of the invention. Accordingly, the scope of theinvention should not be limited by what has thus far been described, butby the appended claims and their legal equivalents.

What is claimed is:
 1. A SCOL target comprising a single cell havingperiodic structures at a plurality of layers and measuring 2 μm by 2 μmor smaller.
 2. The SCOL target of claim 1, wherein the periodicstructures are at most four pitch bars wide.
 3. The SCOL target of claim2, wherein the periodic structures are two pitch bars wide.
 4. The SCOLtarget of claim 1, placed in-die on a corresponding wafer.
 5. The SCOLtarget of claim 1, wherein the periodic structures are gratings.
 6. TheSCOL target of claim 5, further comprising at least one intermediatelayer between the plurality of layers.
 7. The SCOL target of claim 1,wherein the single cell is configured to be illuminated with a spotdiameter less than 1 μm.
 8. The SCOL target of claim 7, wherein anumerical aperture for the spot diameter is greater than ⅓.
 9. The SCOLtarget of claim 1, wherein the single cell is configured to beilluminated at multiple spot locations.
 10. The SCOL target of claim 9,wherein the multiple spot locations are within a pitch of at least oneof the periodic structures.
 11. The SCOL target of claim 1, wherein theperiodic structures are aligned.
 12. The SCOL target of claim 1, whereinthe periodic structures are configured to provide zeroth and first ordermixing.
 13. The SCOL target of claim 1, wherein the periodic structuresare configured to provide overlap between the zeroth order and the firstorder in measured signals from the periodic structures.